Department of Applied Mathematics & Physics, Kyoto University

Technical Report 2001-012 (November 15, 2001)

A New Relaxation Method for Mathematical Programs with Complementarity Constraints
by Gui-Hua Lin and Masao Fukushima

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In this paper, we present a new relaxation method for mathematical programs with complementarity constraints. Based on the fact that a variational inequality problem defined on a simplex can be represented by a finite number of inequalities, we use an expansive simplex instead of the nonnegative orthant involved in the complementarity constraints. We then remove some inequalities and obtain a standard nonlinear program. Constraint qualification or the Mangasarian-Fromovitz constraint qualification holds for the relaxed problem under some mild conditions. We also consider a limiting behavior of the relaxed problem. In particular, we show that any accumulation point of stationary points of the relaxed problems is a weakly stationary point of the original problem and if the function involved in the complementarity constraints does not vanish at this point, it is C-stationary. Furthermore, under some suitable conditions, it is B-stationary.